Hybrid Optimal Method for Design of Biplanar Gradient Coils for Field Gradient Elimination in Magnetic Shielding Rooms

The conventional target field method (TFM) for the design of the biplanar gradient coils aims at the desired magnitude field, resulting in large gradient inhomogeneities. A hybrid method combining the improved TFM and adaptive moment estimation (Adam) algorithm is proposed. The design of biplanar gradient coils is treated as a stochastic optimization problem and the desired gradients are set directly. The regularization coefficient is optimized by the Adam algorithm to minimize the gradient inhomogeneities calculated from the discrete windings. Through numerical and finite-element simulation, the optimization effect and robustness of this hybrid method are verified. At last, a pair of <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\boldsymbol {d\!B_{x}/dz}$ </tex-math></inline-formula> gradient coils with a simple structure is manufactured and tested. In the target region with a side length of 0.3 m, the <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\boldsymbol {d\!B_{x}/dz}$ </tex-math></inline-formula> gradient and the total magnetic field are reduced by up to 99.8% and 55.2%, respectively. The variation of <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\boldsymbol {B_{x}}$ </tex-math></inline-formula> is constrained within 2 nT.